Question

graph $y = \frac{4}{5}x - 7$.

Explanation:

Step1: Identify the slope-intercept form

The equation \( y=\frac{4}{5}x - 7 \) is in slope - intercept form \( y = mx + b \), where \( m=\frac{4}{5} \) (slope) and \( b=-7 \) (y - intercept).

Step2: Find the y - intercept

The y - intercept \( b=-7 \), so the line crosses the y - axis at the point \( (0,-7) \).

Step3: Use the slope to find another point

The slope \( m = \frac{4}{5}=\frac{\text{rise}}{\text{run}} \). From the y - intercept \( (0,-7) \), we can rise 4 units (since the numerator of the slope is 4) and run 5 units to the right (since the denominator of the slope is 5). So we move from \( (0,-7) \) to \( (0 + 5,-7 + 4)=(5,-3) \).

Step4: Graph the line

Plot the points \( (0,-7) \) and \( (5,-3) \) (or other points found using the slope) and draw a straight line through them. The given graph in the problem is incorrect as it does not represent the line \( y=\frac{4}{5}x - 7 \). The correct graph should have a y - intercept at \( (0,-7) \) and a slope of \( \frac{4}{5} \).

Answer:

To graph \( y=\frac{4}{5}x - 7 \):

1. Plot the y - intercept at \( (0,-7) \).
2. Use the slope \( \frac{4}{5} \) to find another point: from \( (0,-7) \), move 5 units right and 4 units up to get \( (5,-3) \).
3. Draw a straight line through \( (0,-7) \) and \( (5,-3) \) (and other points found using the slope). The given graph in the problem is incorrect; the correct line has a y - intercept at \( (0, - 7) \) and a positive slope of \( \frac{4}{5} \).